Identity economics is bad economics. The excellent Nick Rowe puts it well:
Animals can be divided into Carnivores and Non-Carnivores: A = C + NC. Therefore, if we add some wolves to an island of sheep, the number of animals on that island will increase.
It’s easy to see why that argument might not be right. Wolves kill sheep. But if you didn’t know that fact about wolves and sheep, the argument looks very appealing. But the equation A = C + NC tells us absolutely nothing about the world; it’s an accounting identity that is true by definition. The only thing it tells you is how I have chosen to divide up the world into parts. And I can choose an infinite number of different ways to divide the world up into parts.
Here are two more examples:
1. Y = C + I + G + X – M. Therefore an increase in Government spending will increase GDP.
2. Y = C + S + T. Therefore an increase in Taxes will increase GDP.
My guess is that you are much more uncomfortable with the second of those two examples than the first. You have probably seen the first argument before, but have probably not seen the second. But they are both equally correct accounting identities and are both equally rubbish arguments.
As Nick notes, the identities we write down frame our thinking. Write an identity in a different way to check whether the frame really fits.